Trouble with all of this is we don't know how load the OP has it in room. I think this is fundamental in this instance as opposed to discussions of the texture of tone when sharing clips gives a very good comparison. If the reference amp / Kemper setup takes the paint off the wall when he hits it hard anyone trying to come up with a equivalent Axe patch would need to do the same. And of course, if it's made into a sound clip, it would need to be played back at a similar volume.
If the CLR is cranked up so loud is really loud with the Kemper, what fraction of loud is obtained by hitting the strings at light, med and hard pressures when the Axe is used. This might give us some clue as to what's going on...if it's really dynamics.
Prompted by Hysteria's comment:
Here are a few suggestions:
1) Send an audio clip and patch of your 'best dynamic yet' AFII patch
2) Send an audio clip of your desired KPA '65 patch
3) Wait for some gurus to make specific suggestions/patch-mods and then try them (one, by one)
Here is a couple of comments:
a) the perceived difference in behavior between the AFII and KPA may actually be acoustically driven and different EQ-ing between AFII and KPA patches may contribute (room response and speaker location may have been altered so make sure everything stays-put while this trial/comparison phase is completed otherwise your results may be meaningless: same position of speakers, same playing position, same relative volume on CLR, etc.).
b) this seems to be the standard 'life after the microphone' results that the AFII so ably provides versus some of the usual desired 'amp in the room' sound some folks find 'lacking' (although, 'life after the microphone' is the environment in which most professional musicians operate and it never affects their performance or enjoyment for playing
).
EDIT:
I appreciate where 5150 is coming from about thud/punch/rumble being low-end phenomena, however, there are some well known psychoacoustic effects where high-frequency boosting also cause a *perceived* boost in the low-end (off the top my head, I believe 12dB boost 10k produces something like a *perceived* 2dB boost at 100Hz or somewhere along those lines).
Another suggestion - in your AFII amplifier modifiers switch all of your resistors to Carbon Comp if they aren't already, because if it is dynamics that you are truly seeking then in the 'real world' these would be the best option (if you didn't have to worry about hiss/noise).